Consider another special case in which the inclined plane is vertical (θ=π/2). In this case, for what value of m1 would the acceleration of the two blocks be equal to zero? Express your answer in terms of some or all of the variables m2 and g.

Consider another special case in which the inclined plane is vertical (θ=π/2). In this case, for what value of m1 would the acceleration of the two blocks be equal to zero

F - Force

T = Tension

m = mass

a = acceleration

g = gravitational force

Let the given Normal on block 2 = N

and [tex]N = m_2 g \cos \theta[/tex]

and the tension in the given string is said to be [tex]T = m_2 g \sin \theta[/tex]

When the acceleration [tex]a=\frac{F}{m_1}[/tex]

for the said block 1.

It will definite be zero only when Force is zero , F=0.

Here by Force, F

I refer net force on block 1.

Now we know

[tex]F = m_1g-T.[/tex]

It is known that if the said

[tex]\theta=\frac{\pi}{2}[/tex] ,

then Tension [tex]T= m_2g[/tex] [tex][since \sin(\pi/2) = 1][/tex],

Now making [tex]"F = m_1g - m_2g"[/tex]

So If we are to make Force equal to zero

[tex]F=0 => m_1g = m_2g \ or \ m_1 = m_2[/tex]